The engine of a small and unmanned airplane produces a known and specific sound frequency (not given). A stationary sound detection device observes that the known emitted sound frequency is 90% of the perceived sound frequency. Relative to the detection device, in which direction and at what velocity is the plane moving

the source (plane) moves away from the observer ,     v_{s} = 38.2 m / s

Explanation:

This is an exercise in the Doppler effect, which is the change in frequency due to the relative movement of the source and the observer; in this case the observer the sound detection system that is fixed and the source (plane) is mobile, in this case the relationship that describes the process is

where negative sign is for the source moving towards the observer

It indicates that the frequency of the received sound is 90% of the emitted frequency

         f '/ f = 0.90

let's substitute

           0.9 =

            = v / 0.9

The speed of sound is v = 344 m / s, let's substitute

            = 344 / 0.9

           344 \ \frac{-}{+} v_{s} = 382.2

Let's analyze this expression, to fulfill the equation the speed of the source must be positive, therefore the source moves away from the observer

           344 += 382.2

           v_{s} = 382.2 -344

           v_{s} = 38.2 m / s

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